{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance, Part 2: Intro to Quantitative Trading Strategies\n",
    "\n",
    "In the previous article of this series, we focused on using Python and Pandas to \n",
    "\n",
    "1. retrieve financial time-series from free online sources (Yahoo),\n",
    "2. format the data by filling missing observations and aligning them,\n",
    "3. calculate some simple indicators such as rolling moving averages and\n",
    "4. visualise the final time-series.\n",
    "\n",
    "As a reminder, the dataframe containing the three \"cleaned\" price timeseries has the following format:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-03</th>\n",
       "      <td>3.625643</td>\n",
       "      <td>39.334630</td>\n",
       "      <td>1455.219971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-04</th>\n",
       "      <td>3.319964</td>\n",
       "      <td>38.005900</td>\n",
       "      <td>1399.420044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-05</th>\n",
       "      <td>3.368548</td>\n",
       "      <td>38.406628</td>\n",
       "      <td>1402.109985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-06</th>\n",
       "      <td>3.077039</td>\n",
       "      <td>37.120080</td>\n",
       "      <td>1403.449951</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-07</th>\n",
       "      <td>3.222794</td>\n",
       "      <td>37.605172</td>\n",
       "      <td>1441.469971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-10</th>\n",
       "      <td>3.166112</td>\n",
       "      <td>37.879354</td>\n",
       "      <td>1457.599976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-11</th>\n",
       "      <td>3.004162</td>\n",
       "      <td>36.909170</td>\n",
       "      <td>1438.560059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-12</th>\n",
       "      <td>2.823993</td>\n",
       "      <td>35.706986</td>\n",
       "      <td>1432.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-13</th>\n",
       "      <td>3.133722</td>\n",
       "      <td>36.381897</td>\n",
       "      <td>1449.680054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-14</th>\n",
       "      <td>3.253159</td>\n",
       "      <td>37.879354</td>\n",
       "      <td>1465.150024</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                AAPL       MSFT        ^GSPC\n",
       "2000-01-03  3.625643  39.334630  1455.219971\n",
       "2000-01-04  3.319964  38.005900  1399.420044\n",
       "2000-01-05  3.368548  38.406628  1402.109985\n",
       "2000-01-06  3.077039  37.120080  1403.449951\n",
       "2000-01-07  3.222794  37.605172  1441.469971\n",
       "2000-01-10  3.166112  37.879354  1457.599976\n",
       "2000-01-11  3.004162  36.909170  1438.560059\n",
       "2000-01-12  2.823993  35.706986  1432.250000\n",
       "2000-01-13  3.133722  36.381897  1449.680054\n",
       "2000-01-14  3.253159  37.879354  1465.150024"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "data = pd.read_pickle('./data.pkl')\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have also calculated the rolling moving averages of these three timeseries as follows. Note that when calculating the $M$ days moving average, the first $M-1$ are not valid, as $M$ prices are required for the first moving average data point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-03</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-04</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-05</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-06</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-07</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            AAPL  MSFT  ^GSPC\n",
       "2000-01-03   NaN   NaN    NaN\n",
       "2000-01-04   NaN   NaN    NaN\n",
       "2000-01-05   NaN   NaN    NaN\n",
       "2000-01-06   NaN   NaN    NaN\n",
       "2000-01-07   NaN   NaN    NaN"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating the short-window moving average\n",
    "short_rolling = data.rolling(window=20).mean()\n",
    "short_rolling.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-12-26</th>\n",
       "      <td>110.958205</td>\n",
       "      <td>58.418182</td>\n",
       "      <td>2176.628791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-27</th>\n",
       "      <td>111.047874</td>\n",
       "      <td>58.476117</td>\n",
       "      <td>2177.500190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-28</th>\n",
       "      <td>111.140589</td>\n",
       "      <td>58.532936</td>\n",
       "      <td>2178.244490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-29</th>\n",
       "      <td>111.233698</td>\n",
       "      <td>58.586112</td>\n",
       "      <td>2178.879189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-30</th>\n",
       "      <td>111.315270</td>\n",
       "      <td>58.635267</td>\n",
       "      <td>2179.426990</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  AAPL       MSFT        ^GSPC\n",
       "2016-12-26  110.958205  58.418182  2176.628791\n",
       "2016-12-27  111.047874  58.476117  2177.500190\n",
       "2016-12-28  111.140589  58.532936  2178.244490\n",
       "2016-12-29  111.233698  58.586112  2178.879189\n",
       "2016-12-30  111.315270  58.635267  2179.426990"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculating the short-window moving average\n",
    "long_rolling = data.rolling(window=100).mean()\n",
    "long_rolling.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Building on these results, our ultimate goal will be to design a simple yet realistic trading strategy. However, first we need to go through some of the basic concepts related to quantitative trading strategies, as well as the tools and techniques in the process."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## General considerations about trading strategies\n",
    "\n",
    "There are several ways one can go about when a trading strategy is to be developed. One approach would be to use the price time-series directly and work with numbers that correspond to some monetary value. For example, a researcher could be working with time-series expressing the price of a given stock, like the time-series we used in the previous article. Similarly, if working with fixed income instruments, e.g. bonds, one could be using a time-series expressing the price of the bond as a percentage of a given reference value, in this case the par value of the bond. Working with this type of time-series can be more intuitive as people are used to thinking in terms of prices. However, price time-series have some drawbacks. Prices are usually only positive, which makes it harder to use models and approaches which require or produce negative numbers. In addition, price time-series are usually non-stationary, that is their statistical properties are less stable over time.\n",
    "\n",
    "An alternative approach is to use time-series which correspond not to actual values but changes in the monetary value of the asset. These time-series can and do assume negative values and also, their statistical properties are usually more stable than the ones of price time-series. The most frequently used forms used are relative returns defined as\n",
    "\n",
    "\\begin{equation}\n",
    "r_{\\text{relative}}\\left(t\\right) = \\frac{p\\left(t\\right) - p\\left(t-1\\right)}{p\\left(t-1\\right)}\n",
    "\\end{equation}\n",
    "\n",
    "and log-returns defined as\n",
    "\n",
    "\\begin{equation}\n",
    "r\\left(t\\right) = \\log\\left( \\frac{p\\left(t\\right)}{p\\left(t-1\\right)} \\right)\n",
    "\\end{equation}\n",
    "\n",
    "where $p\\left(t\\right)$ is the price of the asset at time $t$. For example, if $p\\left(t\\right) = 101$ and $p\\left(t-1\\right) = 100$ then $r_{\\text{relative}}\\left(t\\right) = \\frac{101 - 100}{100} = 1\\%$.\n",
    "\n",
    "There are several reasons why log-returns are being used in the industry and some of them are related to long-standing assumptions about the behaviour of asset returns and are out of our scope. However, what we need to point out are two quite interesting properties. Log-returns are additive and this facilitates treatment of our time-series, relative returns are not. We can see the additivity of log-returns in the following equation.\n",
    "\n",
    "\\begin{equation}\n",
    "r\\left(t_1\\right) + r\\left(t_2\\right) =  \\log\\left( \\frac{p\\left(t_1\\right)}{p\\left(t_0\\right)} \\right) + \n",
    "\\log\\left( \\frac{p\\left(t_2\\right)}{p\\left(t_1\\right)} \\right) = \\log\\left( \\frac{p\\left(t_2\\right)}{p\\left(t_0\\right)} \\right)\n",
    "\\end{equation}\n",
    "\n",
    "which is simply the log-return from $t_0$ to $t_2$. Secondly, log-returns are approximately equal to the relative returns for  values of $\\frac{p\\left(t\\right)}{p\\left(t-1\\right)}$ sufficiently close to $1$. By taking the 1st order Taylor expansion of $\\log\\left( \\frac{p\\left(t\\right)}{p\\left(t-1\\right)} \\right)$ around $1$, we get\n",
    "\n",
    "\\begin{equation}\n",
    "\\log\\left( \\frac{p\\left(t\\right)}{p\\left(t-1\\right)} \\right) \\simeq \\log\\left(1\\right) + \n",
    "\\frac{p\\left(t\\right)}{p\\left(t-1\\right)} - 1 = r_{\\text{relative}}\\left(t\\right)\n",
    "\\end{equation}\n",
    "\n",
    "Both of these are trivially calculated using Pandas as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-03</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-04</th>\n",
       "      <td>-0.084310</td>\n",
       "      <td>-0.033780</td>\n",
       "      <td>-0.038345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-05</th>\n",
       "      <td>0.014634</td>\n",
       "      <td>0.010544</td>\n",
       "      <td>0.001922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-06</th>\n",
       "      <td>-0.086538</td>\n",
       "      <td>-0.033498</td>\n",
       "      <td>0.000956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-07</th>\n",
       "      <td>0.047369</td>\n",
       "      <td>0.013068</td>\n",
       "      <td>0.027090</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                AAPL      MSFT     ^GSPC\n",
       "2000-01-03       NaN       NaN       NaN\n",
       "2000-01-04 -0.084310 -0.033780 -0.038345\n",
       "2000-01-05  0.014634  0.010544  0.001922\n",
       "2000-01-06 -0.086538 -0.033498  0.000956\n",
       "2000-01-07  0.047369  0.013068  0.027090"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Relative returns\n",
    "returns = data.pct_change(1)\n",
    "returns.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-03</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-04</th>\n",
       "      <td>-0.088078</td>\n",
       "      <td>-0.034364</td>\n",
       "      <td>-0.039099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-05</th>\n",
       "      <td>0.014528</td>\n",
       "      <td>0.010489</td>\n",
       "      <td>0.001920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-06</th>\n",
       "      <td>-0.090514</td>\n",
       "      <td>-0.034072</td>\n",
       "      <td>0.000955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-07</th>\n",
       "      <td>0.046281</td>\n",
       "      <td>0.012984</td>\n",
       "      <td>0.026730</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                AAPL      MSFT     ^GSPC\n",
       "2000-01-03       NaN       NaN       NaN\n",
       "2000-01-04 -0.088078 -0.034364 -0.039099\n",
       "2000-01-05  0.014528  0.010489  0.001920\n",
       "2000-01-06 -0.090514 -0.034072  0.000955\n",
       "2000-01-07  0.046281  0.012984  0.026730"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Log returns - First the logarithm of the prices is taken and the the difference of consecutive (log) observations\n",
    "log_returns = np.log(data).diff()\n",
    "log_returns.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since log-returns are additive, we can create the time-series of cumulative log-returns defined as\n",
    "\n",
    "\\begin{equation}\n",
    "c\\left(t\\right) = \\sum_{k=1}^t r\\left(t\\right)\n",
    "\\end{equation}\n",
    "\n",
    "The cumulative log-returns and the total relative returns from 2000/01/01 for the three time-series can be seen below. Note that although log-returns are easy to manipulate, investors are accustomed to using relative returns. For example, a log-return of $1$ does not mean an investor has doubled the value of his portfolio. A relative return of $1 = 100\\%$ does! Converting between the cumulative log-return $c\\left(t\\right)$ and the total relative return $c_{\\text{relative}}\\left(t\\right) = \\frac{p\\left(t\\right) - p\\left(t_o\\right)}{p\\left(t_o\\right)}$ is simple\n",
    "$$ c_{\\text{relative}}\\left(t\\right) = e^{c\\left(t\\right)} - 1 $$\n",
    "\n",
    "For those who are wondering if this is correct, yes it is. If someone had bought $\\$1000$ worth of AAPL shares in January 2000, her/his portfolio would now be worth over $\\$30,000$. If only we had a time machine... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kKyuL9u3b4+3tjZ+fH507d6ZVq1akpaXx2GOPsW/fPnx8fAgNDeXDDz88bXmZ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6AAAg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\n6TXGxFR6xRljJgI1jzVxKQHutNb2B8YANxtj+gP3ArOttb2B2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fOANC/jOAt431pbaK3d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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2054b96cb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=[16,9])\n",
    "\n",
    "ax = fig.add_subplot(2,1,1)\n",
    "\n",
    "for c in log_returns:\n",
    "    ax.plot(log_returns.index, log_returns[c].cumsum(), label=str(c))\n",
    "\n",
    "ax.set_ylabel('Cumulative log returns')\n",
    "ax.legend(loc='best')\n",
    "ax.grid()\n",
    "\n",
    "ax = fig.add_subplot(2,1,2)\n",
    "\n",
    "for c in log_returns:\n",
    "    ax.plot(log_returns.index, 100*(np.exp(log_returns[c].cumsum()) - 1), label=str(c))\n",
    "\n",
    "ax.set_ylabel('Total relative returns (%)')\n",
    "ax.legend(loc='best')\n",
    "ax.grid()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is a quantitative trading strategy?\n",
    "\n",
    "Our goal is to develop a toy trading strategy, but what does the term \"quantitative trading strategy\" actually mean? In this section we will give a definition that will guide us in our long-term goal. \n",
    "\n",
    "Assume we have at our disposal a certain amount of dollars, $N$, which we are interested to invest. We have at our disposal a set of $K$ assets from which we can buy and sell freely any arbitrary amount. Our goal is to derive weights $w_i\\left(t\\right), i = 1, \\ldots, K$ such that \n",
    "\n",
    "$$w_i\\left(t\\right) \\in \\mathbb{R} \\ \\text{and} \\ \\sum_{i=1}^K w_i\\left(t\\right) \\leq 1$$\n",
    "\n",
    "so that an amount of dollars equal to $w_i\\left(t\\right) N$ is invested at time $t$ on asset $i$. \n",
    "\n",
    "The inequality condition signifies $\\sum_{i=1}^K w_i\\left(t\\right) \\leq 1$ that the maximum amount we can invest is equal to amount of dollars we have, that is $N$.\n",
    "\n",
    "<p class=\"example\">For example, assume we can invest in $2$ instruments only and that $N=\\$1000$. The goal is to derive two weights $w_1\\left(t\\right)$ and $w_2\\left(t\\right)$.\n",
    "If at some point $w_1\\left(t\\right) = 0.4$ and $w_2\\left(t\\right) = 0.6$, this means that we have invested $w_1\\left(t\\right)N = \\$400$ in asset $1$ and $w_2\\left(t\\right)N = \\$600$ in asset $2$. Since we only have $\\$1000$, we can only invest up to that much which means that\n",
    "$$w_1\\left(t\\right)N + w_2\\left(t\\right)N \\leq N \\Rightarrow w_1\\left(t\\right) + w_2\\left(t\\right) < 1$$.\n",
    "</p>\n",
    "\n",
    "Note that since we have allowed $w_i\\left(t\\right)$ to be any real number, we are implying that we are allowed to have negative weights. Negative weights imply that we have sold a given asset short. Selling short an asset means selling an asset we do not currently hold and receiving its value in cash. Selling short is different than selling an asset we already own, which is called selling long. \n",
    "\n",
    "The mechanics behind this can be complicated and are usually subject to regulatory scrutiny. However, on a high level, it involves borrowing the asset from a third party and then selling it to the buyer. Since at some point the asset needs to be returned to the party from which it was borrowed, the short position needs to be closed. This is achieved by buying the asset back from the original buyer or any other willing seller. For the purpose of this article it will be assumed that selling an asset short can be accomplished at no added cost, an assumption which is not true.\n",
    "\n",
    "<span class=\"note\">More on selling long vs. selling short [here](http://www.investopedia.com/ask/answers/100314/whats-difference-between-long-and-short-position-market.asp).</span>\n",
    "\n",
    "The assuming that the weights can be unbounded is not realistic. For example, based on the definition given above we could sell short an amount of AAPL shares of value equal to $N$. This means that, for now, we have at our disposal an additional $N$ dollars to invest from the short sale. Thus, together with our original $N$ dollars, we can the purchase shares of MSFT worth $2N$ dollars. In our framework, this translates to $w_{\\text{AAPL}}=-1$ and $w_{\\text{MSFT}}=2$. In theory, the weights could be $-999$ and $1000$ respectively. However, an increase in the absolute values of the weights leads to an increase in the risk of our portfolio for reasons we will see further down this series of tutorials. Therefore, when developing our trading strategy, appropriate thresholds will be imposed on the weights $w_i\\left(t\\right)$.\n",
    "\n",
    "A final note has to do with cash. Any portfolio will at some point in time include cash. In the aforementioned setup if at any point in time $W = \\sum_{i=1}^K w_i\\left(t\\right) < 1$, then it means that our portfolio includes $\\left(1-W\\right)N$ dollars in cash. Of course, if $W<0$, our net position is short, which means we are currently holding more than $N$ dollars which is the initial value of the portfolio."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Putting it all together\n",
    "\n",
    "For the remaining of this series of tutorials we will assume (unless explicitly stated) that $N=\\$1$. This will allow us to simplify the notation and all calculations and only deal with the weights $w_i\\left(t\\right)$ of the strategy which will be pure numbers. We can always convert back to a monetary value by simply multiplying our dimensionless weights with $N$, the value of the portfolio in dollars (or any other currency of interest). We will also assume that daily returns of the different assets are small enough, so that log-returns are roughly equal to relative returns. Thus, in what follows we will be using the log-returns. \n",
    "\n",
    "Assume that somehow we have what we think is a promising strategy, which is simply a vector\n",
    "\n",
    "\\begin{equation}\n",
    "\\vec{w}\\left(t\\right) = \\left[ w_1\\left(t\\right), w_2\\left(t\\right), \\ldots, w_K\\left(t\\right) \\right]^T \\in \\mathbb{R}^{K \\times 1}\n",
    "\\end{equation}\n",
    "\n",
    "Then, if $\\vec{r}\\left(t\\right)$ is a column vector of relative returns for the assets in the portfolio, the total log-return $r_p\\left(t\\right)$ for each $t$ is simply\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{aligned}\n",
    "r_p\\left(t\\right) &= \\vec{w}^T\\left(t\\right) \\vec{r}\\left(t\\right) \\\\\n",
    "&= w_1\\left(t\\right) r_1\\left(t\\right) + \\ldots + w_K\\left(t\\right) r_K\\left(t\\right)\n",
    "\\end{aligned}\n",
    "\\end{equation}\n",
    "\n",
    "Let us assume we are are using the last day in our dataset and $w_1 = w_2 = w_3 = \\frac{1}{3}$. Then:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2016-12-30 00:00:00</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AAPL</th>\n",
       "      <td>-0.007826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSFT</th>\n",
       "      <td>-0.012156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>^GSPC</th>\n",
       "      <td>-0.004648</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       2016-12-30\n",
       "AAPL    -0.007826\n",
       "MSFT    -0.012156\n",
       "^GSPC   -0.004648"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Last day returns. Make this a column vector\n",
    "r_t = log_returns.tail(1).transpose()\n",
    "r_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2016-12-30 00:00:00</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AAPL</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MSFT</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>^GSPC</th>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       2016-12-30\n",
       "AAPL     0.333333\n",
       "MSFT     0.333333\n",
       "^GSPC    0.333333"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Weights as defined above\n",
    "weights_vector = pd.DataFrame(1 / 3, index=r_t.index, columns=r_t.columns)\n",
    "weights_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2016-12-30 00:00:00</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-12-30</th>\n",
       "      <td>-0.00821</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            2016-12-30\n",
       "2016-12-30    -0.00821"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Total log_return for the portfolio is:\n",
    "portfolio_log_return = weights_vector.transpose().dot(r_t)\n",
    "portfolio_log_return"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If computer memory is not an issue, a very fast way of computing the portfolio returns for all days, $t = 1, \\ldots, T$ is the following: \n",
    "\n",
    "Assume that $\\mathbf{R} \\in \\mathbb{R}^{T \\times K}$ is a matrix, the $t$th row of which is the row vector $\\vec{r}\\left(t\\right)^T$. Similarly, $\\mathbf{W} \\in \\mathbb{R}^{T \\times K}$ is a matrix, the $t$th row of which is the row vector $\\vec{w}\\left(t\\right)^T$. Then if $\\vec{r}_p = \\left[ r_p\\left(1\\right), \\ldots, r_p\\left(T\\right) \\right]^T \\in \\mathbf{R}^{T \\times 1}$ is a column vector of all portfolio returns, we have\n",
    "\n",
    "$$\\vec{r}_p = \\text{diag}\\left\\{ \\mathbf{W} \\mathbf{R}^T \\right\\}$$\n",
    "\n",
    "where $\\text{diag}\\left\\{A \\right\\}$ is the diagonal of a matrix $\\mathbf{A}$. The diagonal extraction is required because only in the diagonal the weights and log-returns vectors are properly time-aligned."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An example\n",
    "\n",
    "To illustrate the concepts of the previous section, let us consider a very simple trading strategy, where the investor splits his investments equally among all three assets we have been looking at. That is:\n",
    "\n",
    "$$ w_{\\text{AAPL}} = w_{\\text{MSFT}} = w_{\\text{^GSPC}} = \\frac{1}{3} $$\n",
    "\n",
    "In this case matrix $\\mathbf{W}$ will be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-12-26</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-27</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-28</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-29</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-30</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                AAPL      MSFT     ^GSPC\n",
       "2016-12-26  0.333333  0.333333  0.333333\n",
       "2016-12-27  0.333333  0.333333  0.333333\n",
       "2016-12-28  0.333333  0.333333  0.333333\n",
       "2016-12-29  0.333333  0.333333  0.333333\n",
       "2016-12-30  0.333333  0.333333  0.333333"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights_matrix = pd.DataFrame(1 / 3, index=data.index, columns=data.columns)\n",
    "weights_matrix.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix $\\mathbf{R}$ is simply our log-returns dataframe defined before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>^GSPC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-03</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-04</th>\n",
       "      <td>-0.088078</td>\n",
       "      <td>-0.034364</td>\n",
       "      <td>-0.039099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-05</th>\n",
       "      <td>0.014528</td>\n",
       "      <td>0.010489</td>\n",
       "      <td>0.001920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-06</th>\n",
       "      <td>-0.090514</td>\n",
       "      <td>-0.034072</td>\n",
       "      <td>0.000955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-07</th>\n",
       "      <td>0.046281</td>\n",
       "      <td>0.012984</td>\n",
       "      <td>0.026730</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                AAPL      MSFT     ^GSPC\n",
       "2000-01-03       NaN       NaN       NaN\n",
       "2000-01-04 -0.088078 -0.034364 -0.039099\n",
       "2000-01-05  0.014528  0.010489  0.001920\n",
       "2000-01-06 -0.090514 -0.034072  0.000955\n",
       "2000-01-07  0.046281  0.012984  0.026730"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_returns.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, the portfolio returns are calculated as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2000-01-03 00:00:00</th>\n",
       "      <th>2000-01-04 00:00:00</th>\n",
       "      <th>2000-01-05 00:00:00</th>\n",
       "      <th>2000-01-06 00:00:00</th>\n",
       "      <th>2000-01-07 00:00:00</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-03</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.053847</td>\n",
       "      <td>0.008979</td>\n",
       "      <td>-0.04121</td>\n",
       "      <td>0.028665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-04</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.053847</td>\n",
       "      <td>0.008979</td>\n",
       "      <td>-0.04121</td>\n",
       "      <td>0.028665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-05</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.053847</td>\n",
       "      <td>0.008979</td>\n",
       "      <td>-0.04121</td>\n",
       "      <td>0.028665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-06</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.053847</td>\n",
       "      <td>0.008979</td>\n",
       "      <td>-0.04121</td>\n",
       "      <td>0.028665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-07</th>\n",
       "      <td>NaN</td>\n",
       "      <td>-0.053847</td>\n",
       "      <td>0.008979</td>\n",
       "      <td>-0.04121</td>\n",
       "      <td>0.028665</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            2000-01-03  2000-01-04  2000-01-05  2000-01-06  2000-01-07\n",
       "2000-01-03         NaN   -0.053847    0.008979    -0.04121    0.028665\n",
       "2000-01-04         NaN   -0.053847    0.008979    -0.04121    0.028665\n",
       "2000-01-05         NaN   -0.053847    0.008979    -0.04121    0.028665\n",
       "2000-01-06         NaN   -0.053847    0.008979    -0.04121    0.028665\n",
       "2000-01-07         NaN   -0.053847    0.008979    -0.04121    0.028665"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initially the two matrices are multiplied. Note that we are only interested in the diagonal, \n",
    "# which is where the dates in the row-index and the column-index match.\n",
    "temp_var = weights_matrix.dot(log_returns.transpose())\n",
    "temp_var.head().ix[:, 0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2016-12-26    0.000000\n",
       "2016-12-27    0.003070\n",
       "2016-12-28   -0.005753\n",
       "2016-12-29   -0.000660\n",
       "2016-12-30   -0.008210\n",
       "Freq: B, dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The numpy np.diag function is used to extract the diagonal and then\n",
    "# a Series is constructed using the time information from the log_returns index\n",
    "portfolio_log_returns = pd.Series(np.diag(temp_var), index=log_returns.index)\n",
    "portfolio_log_returns.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that these returns are only estimates because of our use of log-returns instead of relative returns. However, for most practical purposes the difference is negligible. Let us see what our cumulative log returns and the total relative returns for this portfolio look."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EQtsY13nbJ6a4jmtX4rxgEZFT5UnCWxOIwDmMGSAcqGWtzTPGZHktMhERERHh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\nW5Rby9w1e4kwsO1QHrdM60dpWTlRkRGev68/f7GVVbuy/F5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BUxe6hiy/dt0Ez7HPnXm+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\nlekzeQEJDSJ5e1RvluzI4OWV+Ty3cj5Xt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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2054c25d080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "total_relative_returns = (np.exp(portfolio_log_returns.cumsum()) - 1)\n",
    "\n",
    "fig = plt.figure(figsize=[16,9])\n",
    "ax = fig.add_subplot(2, 1, 1)\n",
    "ax.plot(portfolio_log_returns.index, portfolio_log_returns.cumsum())\n",
    "ax.set_ylabel('Portfolio cumulative log returns')\n",
    "ax.grid()\n",
    "ax = fig.add_subplot(2, 1, 2)\n",
    "ax.plot(total_relative_returns.index, 100 * total_relative_returns)\n",
    "ax.set_ylabel('Portfolio total relative returns (%)')\n",
    "ax.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this simple investing strategy would yield a total return of more than $325\\%$ in the course of almost $16$ years. \n",
    "\n",
    "How does this translate to a yearly performance? Since we have kept all weekdays in our portfolio, there are $52 \\times 5 = 260$ weekdays each year. There are $4435$ days in our simulation which corresponds roughly to $16.92$ years. We will be calculating the average geometric return, that is an average return $\\bar{r}$ which when compounded for $16.92$ years will produce the total relative return of $325.14\\%$. So we need to solve:\n",
    "\n",
    "\\begin{equation}\n",
    "\\left(1 + \\bar{r}\\right)^{16.92} = 1 + 3.2514\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total portfolio return is: 325.14%\n",
      "Average yearly return is:  8.85%\n"
     ]
    }
   ],
   "source": [
    "# Calculating the time-related parameters of the simulation\n",
    "days_per_year = 52 * 5\n",
    "total_days_in_simulation = data.shape[0]\n",
    "number_of_years = total_days_in_simulation / days_per_year\n",
    "\n",
    "# The last data point will give us the total portfolio return\n",
    "total_portfolio_return = total_relative_returns[-1]\n",
    "# Average portfolio return assuming compunding of returns\n",
    "average_yearly_return = (1 + total_portfolio_return)**(1 / number_of_years) - 1\n",
    "\n",
    "print('Total portfolio return is: ' +\n",
    "      '{:5.2f}'.format(100 * total_portfolio_return) + '%')\n",
    "print('Average yearly return is: ' +\n",
    "      '{:5.2f}'.format(100 * average_yearly_return) + '%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What next?\n",
    "\n",
    "Our strategy is a very simple example of a buy-and-hold strategy. The investor simply splits up the available funds in the three assets and keeps the same position throughout the period under investigation. Although simple, the strategy does produce a healthy $8.85\\%$ per year. \n",
    "\n",
    "However, the simulation is not completely accurate. Let us not forget that we have used ALL weekdays in our example, but we do know that on some days the markets are not trading. This will not affect the strategy we presented as the returns on the days the markets are closed are 0, but it may potentially affect other types of strategies. Furthermore, the weights here are constant over time. Ideally, we would like weights that change over time so that we can take advantage of price swings and other market events.\n",
    "\n",
    "Also, we have said nothing at all about the risk of this strategy. Risk is the most important consideration in any investment strategy and is closely related to the expected returns. In what follows, we will start designing a more complex strategy, the weights of which will not be constant over time. At the same time we will start looking into the risk of the strategy and present appropriate metrics to measure it. Finally, we will look into the issue of optimizing  the strategy parameters and how this can improve our return to risk profile."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": []
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